Chaos in Kuramoto Oscillator Networks

Abstract

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this record.Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme can exhibit chaotic dynamics as conjectured by Ott and Antonsen [Chaos, 18, 037113 (2008)]. These chaotic mean field dynamics arise universally across network size, from the continuum limit of infinitely many oscillators down to very small networks with just two oscillators per population. Hence, complicated dynamics are expected even in the simplest description of oscillator networks.The authors would like to thank J Engelbrecht, R Mirollo, A Politi, and M Wolfrum for helpful discussions and F Peter for careful reading of the manuscript. CB would like to acknowledge the warm hospitality at DTU. Research conducted by EAM is partially supported by the Dynamical Systems Interdisciplinary Network, University of Copenhagen. CB has received partial funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007–2013) under REA grant agreement no. 626111